Electronic polarons, cumulants and doubly dynamical mean field theory: Theoretical spectroscopy for correlated and less correlated materials

Abstract

The use of effective local Coulomb interactions that are dynamical, that is, frequencydependent, is an efficient tool to describe the effect of long-range Coulomb interactions and screening thereof in solids. The dynamical character of the interaction introduces the coupling to screening degrees of freedom such as plasmons or particle-hole excitations into the many-body description. We summarize recent progress using these concepts, putting emphasis on dynamical mean field theory (DMFT) calculations with dynamical interactions ("doubly dynamical mean field theory"). We discuss the relation to the combined GW+DMFT method and its simplified version "Screened Exchange DMFT", as well as the cumulant schemes of many-body perturbation theory. On the example of the simple transition metal SrVO 3 , we illustrate the mechanism of the appearance of plasmonic satellite structures in the spectral properties, and discuss implications for the low-energy electronic structure. Theoretical Spectroscopy: from many-body perturbation theory to dynamical Hubbard interactionsDetermining the behavior of a single electron in a periodic potential, created for example by the ions in a cristalline solid, is a textbook exercise of quantum mechanics. Determining the wave function of all the electrons in the solid, however, is an intractable many-body problem. The Pauli principle imposes full antisymmetry under exchange of any two electrons to this object, and electronic Coulomb interactions prevent it from being a simple Slater determinant.The good news is that in practice the knowledge of the full many-body wave function of the inhomogeneous electron gas in the solid is barely necessary: the relevant electronic properties are determined by the low-energy response to external perturbations, and the knowledge of these low-energy excitations requires much less information than the full ground-state wave function. In this sense, solid state spectroscopies are a most efficient means for characterizing the properties of a solid state system. An important example are photoemission experimentsangle-resolved or angle-integrated -where information about the electron removal and addition spectra are obtained. Within the simplest possible model for the photoemission process, the so-called "three-step model", the photocurrent can be expressed in terms of the one-particle spectral function A(k, ω) = − 1 π T r G(k, ω), and computing this quantity from first principles, that is, without adjustable parameters, is one of the central challenges of modern theoretical spectroscopy.Important progress has been achieved over the last decades within many-body perturbation theory: a first order expansion of the many-body self-energy Σ in the screened Coulomb interaction W [1, 2] leads to a conceptually simple approximation Σ = iGW which can be calculated within realistic electronic structure codes based on density functional theory (DFT). For reviews of 1 arXiv:1512.08499v1 [cond-mat.str-el]

Green’s function methods for excited states and x-ray spectra of functional materials

“…Open shell systems pose further challenges [73][74][75][76]. Nevertheless, the cumulant approach has been found useful for treating correlated behavior in some f-electron materials; the inclusion of plasmon-excitations in conjunction with DMFT [77], and more recently in applications to open-shell systems such as ligand-field atomic multiplets systems [69].…”

Depth-Resolving the Charge Compensation Mechanism from LiNiO2 to NiO2

“…We evidence here that the O 1s satellites are related to plasmonic excitation processes, as determined by constrained random phase approximation (cRPA) calculations of the dynamically screened Coulomb interaction U (ω) . Indeed, plasmonic excitations can be recognized by a divergence of the real part of the U (ω) curve at the plasmon frequency ω p . As shown in Figure h, plasmons were observed at ω p = 8.5 eV for LiNiO 2 and ω p = 8.5 and 11 eV for NiO 2 .…”

“…76 Indeed, plasmonic excitations can be recognized by a divergence of the real part of the U(ω) curve at the plasmon frequency ω p . 77 As shown in Figure 3h, plasmons were observed at ω p = 8.5 eV for LiNiO 2 and ω p = 8.5 and 11 eV for NiO 2 . While a good quantitative agreement is obtained for NiO 2 even at the DFT level, the same cannot be said for LiNiO 2 .…”

Ab initio multiplet plus cumulant approach for correlation effects in x-ray photoelectron spectroscopy

“…The above approximation was inspired by the work in Refs. 6,34 , where a similar product of an atomic Green's function and cumulant form was used to treat plasmon excitations in DMFT. To justify our approach we define a separable model Hamiltonian H = H loc + H bos in which the simplified localized (atomic, ligand field, or cluster) system consists of a limited number of electrons (the 2p and 3d shells for example) interacting with the extended system via quasibosons that characterize the excitations 10 .…”